1. Field of the Invention
The present invention relates to optical proximity correction upon manufacturing of a semiconductor device.
2. Description of Related Art
Advances of semiconductor manufacturing technique in recent years have allowed semiconductors having a minimum fabrication size of 50 nm or less to be manufactured. Such miniaturization has become possible because of advances in fine patterning techniques such as a mask process technique, a photolithography technique, and an etching technique. When an exposure apparatus used an i-line or a g-line, and a pattern size was sufficiently larger than the wavelength of exposure light, a pattern almost faithful to an original LSI pattern could be formed on a wafer by directly transferring on a mask, the LSI pattern to be formed on the wafer by use of electron beam lithography, further transferring a mask pattern on a wafer by a projection optical system, and etching the wafer.
However, along with the pattern miniaturization, it has been difficult to faithfully transfer/form a pattern in each process. Therefore, there arises a problem that an original critical dimension (CD) of an LSI pattern cannot be reproduced as a final critical dimension (CD). In particular, in lithography and etching processes that are most important for finer fabrication, a dimensional accuracy (CD accuracy) of a desired pattern is largely influenced by a layout of other patterns arranged around the desired pattern to be formed.
Therefore, in order to suppress such variation, an optical proximity correction (OPC) technique has been employed in which edge and corner portions of the mask pattern where the variation is significant are preliminarily deformed such that a dimension after fabrication takes a desired value. In this technique, a pattern after development reproduces the original pattern by fundamentally dissecting sides of an original pattern, and minutely moving the dissected sides. Specifically, in Japanese patent No. 3,343,246, an original pattern is dissected, two apexes are inserted in each dissected portion, and a line segment is generated between the two apexes. Thus, the dissected sides are moved without generating a line segment not connected to another line segment. An amount of the movement is determined on the basis of a table called a lookup table in a rule-based OPC, whereas it is recursively determined on the basis of a development (or optical) simulation, i.e., on the basis of trial and error, in a model-based OPC.
In the conventional model-based OPC, all patterns on a plane are decomposed into rectangles having horizontal and vertical sides. If there is no oblique side component, the conventional model-based OPC is well applicable. In the model-based OPC, a movement direction of one side to be moved for correction is characterized by being perpendicular to a direction of the line segment of the side. That is, a pattern to be corrected is set in an orthogonal coordinate system having x- and y-axes, and if the line segment of the side is parallel to the x-axis, the movement direction is parallel to the y-axis, whereas if the line segment of the side is parallel to the y-axis, the movement direction is parallel to the x-axis. Accordingly, if the pattern includes sides parallel to any of the coordinate axes of the orthogonal coordinate system, it is easy to linearly predict and correct a shift amount of the side between a desired position and a calculated position.
Specifically, it is assumed that a mask error enhancement factor (MEEF) is denoted by A, a line segment in the y direction is positioned at x0, and a development position of the side is shifted to X0. When the original side is varied in position as x0±dx, the development position can be predicted as X0±dx×A by linear prediction. When a graphic pattern is complicated, a value of A is unknown. However, if this linearity is used and it is supposed that x1=x0+dx0 and a corresponding development position is X1=X0+dx0×A, A=(X1−X0)/dx0=(X1−X0)/(x1−x0). It can be estimated that dx1 meeting x0=X0+dx1×A is dx1=(x0−X0)×(x1−x0)/(X1−X0).
However, a problem arises when an oblique graphic pattern having oblique sides is present. Considering an LSI circuit layout to be produced, an oblique line often achieves the shortest distance, and if this oblique line is allowed, design is facilitated. In this case, two problems arise in OPC calculations.
A first problem is in that a direction of the oblique side of the oblique graphic pattern and a movement direction of it are not orthogonal to each other, so that a correction amount is different for each side, resulting in difficulty in the linear prediction. In conjunction with this problem, a technique described in Japanese Patent Application Publication (JP-P2005-84280A) is related to the rule-based OPC, and the oblique graphic pattern and horizontal/vertical graphic patterns are distinguished from each other, and a movement amount of a side is changed for each of the graphic patterns. This means that even if the rule-based OPC is replaced by the model-based OPC without modification, a correction amount should be different between the oblique graphic pattern and the horizontal/vertical graphic patterns. In such a method, a defect of an abnormal pattern may be generated upon production of a mask, depending on a condition.
Also, a technique related to the oblique pattern correction of the rule-based OPC is described in Japanese Patent Application Publication (JP-P2001-281836A). In this technique, an oblique graphic pattern is once rotated such that sides thereof are horizontally/vertically directed, and subjected to the same rule-based OPC as in case of correction of horizontal/vertical graphic pattern, and then the corrected graphic pattern is reversely rotated to have an original oblique side. However, if this is applied to the model-based OPC in which the trial-and-error is repeated, the rotation and the reverse rotation are repeated many times, and therefore calculation is time-consuming.
A second problem is in that an oblique line necessarily intersects with a vertical or horizontal line somewhere, and these lines form an acute-angled portion. The optical proximity correction (OPC) is less effective to such an acute-angled portion, and therefore causes a reduction in throughput in electron beam lithography for producing a mask.